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P. Sitko

Publications and source records attributed to P. Sitko.

9 recordsLinked to original sources
arXiv2025

Reducing of system of partial differential equations and generalized symmetry of ordinary differential equations

Symmetry reductions of systems of two nonlinear partial differential equations are studied. We find ansatzes reducing system of partial differential equations to system of ordinary differential equations. The method is applied to system related to Korteweg -- de Vries (KdV) equation, and reaction-diffusion equations. We have also shown the possibility of constructing solution to system of non-evolutionary equations, which contains one or two arbitrary functions.

nlin.SI↗
arXiv1999

On the interaction energy of 2D electron FQHE systems within the Chern-Simons approach

The interaction energy of the two-dimensional electron system in the region of fractional quantum Hall effect is considered within the Chern-Simons composite fermion approach. In the limit when Coulomb interaction is very small comparing to the cyclotron energy the RPA results are obtained for the fillings $ν=1/3, 1/5, 2/3, 2/5, 3/7$ and compared with the exact diagonalization results for small systems (extrapolated for infinite systems). They show very poor agreement suggesting the need for looking for alternative approaches.

cond-mat.mes-hall↗
arXiv1997

The Composite Fermion Hierarchy: Condensed States of Composite Fermion Excitations?

A composite Fermion hierarchy theory is constructed in a way related to the original Haldane picture by applying the composite Fermion (CF) transformation to quasiparticles of Jain states. It is shown that the Jain theory coincides with the Haldane hierarchy theory for principal CF fillings. Within the Fermi liquid approach for few electron systems on the sphere a simple interpretation of many-quasiparticle spectra is given and provides an explanation of failure of CF hierarchy picture when applied to the hierarchical $4/11$ state.

cond-mat.mes-hall↗
arXiv1997

Quantum Hall Spherical Systems: the Filling Fraction

Within the newly formulated composite fermion hierarchy the filling fraction of a spherical quantum Hall system is obtained when it can be expressed as an odd or even denominator fraction. A plot of $ν\frac{2S}{N-1}$ as a function of $2S$ for a constant number of particles (up to N=10001) exhibits structure of the fractional quantum Hall effect. It is confirmed that $ν_e +ν_h=1$ for all particle-hole conjugate systems, except systems with $N_e =N_h$, and $N_e=N_h \pm 1$.

cond-mat.mes-hall↗
arXiv1996

``Fermi Liquid'' Shell Model Approach to Composite Fermion Excitation Spectra in Fractional Quantum Hall States

Numerical results for the energy spectra of $N$ electrons on a spherical surface are used as input data to determine the quasiparticle energies and the pairwise ``Fermi liquid'' interactions of composite Fermion (CF) excitations in fractional quantum Hall systems. The quasiparticle energies and their interactions are then used to determine the energy spectra, $E$ vs total angular momentum $L$, of states containing more than two quasiparticles. The qualitative agreement with the numerical results gives a remarkable new confirmation of the CF picture.

cond-mat↗
arXiv1995

Hartree-Fock ground state of the composite fermion metal

Within the Hartree-Fock approximation the ground state of the composite fermion metal is found. We observe that the single-particle energy spectrum is dominated by the logarithmic interaction exchange term which leads to an infinite jump of the single-particle energy at the Fermi momentum. It is shown that the Hartree-Fock result brings no corrections to the RPA Fermi velocity.

cond-mat↗